mixing formulas questions 1-3

Introduction

  • Presenter: Jim Matt

  • Objectives:

    • Review applications of the mixing formula.

    • Solve examples, with a focus on work color in example seven.

    • Gain proficiency in using the mixing formula for various brewery problems.

Applications of the Mixing Formula

  • Versatile tool in the brewery for solving problems such as:

    • Alcohol correction: Diluting high alcohol beer with water.

    • Caustic makeup: Creating lower concentration caustic solutions.

    • Peracetic acid makeup: Preparing sanitizer solutions.

    • Dilution water calculations.

    • Heat balance issues.

    • Multivariable three-component mixing.

Overview of the Mixing Formula

  • Formula Structure:

    • A × a + B × b = C × c

    • Capital letters (A, B, C): quantities to be mixed.

    • Lowercase letters (a, b, c): corresponding properties (e.g., alcohol by volume).

    • Example units: liters, milliliters, hectoliters.

Example 1: Alcohol Correction Problem

  • Problem: Determine final alcohol percentage when mixing high gravity beer and water.

    • Given:

      • A = 200 hectoliters (high gravity beer)

      • a = 7.15% (alcohol by volume)

      • B = 100 hectoliters (dilution water)

      • b = 0% (alcohol level of water)

      • C = 300 hectoliters (total mixture)

    • Final Property:

      • c = ? (final alcohol percentage)

  • Calculation Steps:

    1. Plug in known quantities:

      • 200 × 7.15 + 0 × 100 = 300c

    2. Isolate c:

      • 1430 = 300c

      • c = 4.77% alcohol by volume

  • Note: Use de-aerated water in industrial processes to avoid increasing dissolved oxygen.

Example 2: Caustic Makeup Problem

  • Problem: How much 30% caustic must be added to raise causticity?

    • Given:

      • A = 200 hectoliters (initial solution)

      • a = 3%

      • B = ? (unknown volume of 30% caustic)

      • b = 30% (caustic concentration to add)

      • C = 4% (desired final concentration)

    • Calculation Steps:

    1. Plug in values:

      • 200 × 3 + 30B = (200 + B) × 4

    2. Solve for B:

      • 600 + 30B = 800 + 4B

      • 26B = 200

      • B = 200/26 = 7.69 hectoliters

Knowledge Check

  • True or False: The mixing formula is a complex equation.

    • Answer: False

    • Reason: It is a simple algebraic formula.

Additional Problem: Mixing Nitric Acid

  • Problem: Volumes needed for 25% nitric acid solution.

    • Given percentage and strength, calculate needed volumes.

    • Answer: 52.6 liters is required.

Example 3: Peroxyacetic Acid Makeup Problem

  • Problem: How to make a 100 part per million solution from a 5.5% solution.

    • Given:

      • Total volume = 1 liter (1,000 milliliters)

      • a = 0 ppm (concentration in water)

      • B = ? (volume of peroxyacetic acid needed)

      • b = 55,000 ppm (concentration of the 5.5% solution)

      • C = 100 ppm (desired concentration)

    • Calculation Steps:

    1. Convert units and set up equations:

      • 0 × (1000 - B) = 0 (zero concentration)

      • 55,000B = 100,000

    2. Solve for B:

      • B = 1.8 milliliters of peroxyacetic acid.

    3. Calculate the amount of water to add:

      • 998.2 milliliters (1000 - 1.8)